Notice how the distance from the focus to any point equals the perpendicular distance from the directrix to that point?

Yea', but you have just a flat wooden surface, some rope, some nails (and a hammer or rock or anything to nail them to the board, right...) and a pencil; you don't have an instrument to measure 90 degrees from directrix.

I mean - it's easy to draw a circle or its section with those materials - you just nail one to the board and tie a rope to it and pencil on the other end - and just draw it... drawing an ellipse is easy as well - you just put two nails, loop the rope and pull it with pencil to draw it as the rope allows no further pull.

With parabola it's not the same - the length changes and you need to measure stuff - that avoids the essence of "stick-and-rope" principle I coconut :) on here...

--------
Also: when you take a paper strip, put it on the flat surface (table), and contract it so it stands up - is it parabola or something else?

It's actually quite simple. Hammer in a nail, tie on the rope to a length that it just touches an edge of the table, draw out a circle from that. The line connecting the edge of the table and the nail will be perpendicular to the edge of the table.

AHAAA - but in that case the line has to move across the length of the edge of the board.
Interactive java applet (at the bottom of the page; pick the red dot and move it left-right):
http://www.ies.co.jp/math/java/conics/draw_parabola/draw_parabola.html [Broken]

I'm wondering, on the other hand, how to draw it without rightangle tool - just by materials I described (nails, rope, pencil, board).

Staff: Mentor

I just got rid of the nail. And the assistant. Just me, the board and the pencil. Very accurate parabola, too!

...What? ...You placed the board vertically, climbed at a height of about 4 meters holding a pencil to your right, and jumped with the board close to your side, so when you fell on your 455 and bounced a bit the pencil left the trail of your bouncing on the board???

====
(Just joking.
Don't get me
serious now.
Had an idea,
laughed and
had to
write it... )

Staff: Mentor

...What? ...You placed the board vertically, climbed at a height of about 4 meters holding a pencil to your right, and jumped with the board close to your side, so when you fell on your 455 and bounced a bit the pencil left the trail of your bouncing on the board???

Try using the string as a measuring tool. Set one piece of it as 1 unit, and try to calculate the y parts from the x. For example, try y = x^2. At x = 1, y = 1. At x = 2, y = 4. You get the idea. Then just play connect the dots with a curved line drawn by hand. I believe it was mentioned earlier as to how to get a perpendicular line.